Quantum annealing and the Schr\"odinger-Langevin-Kostin equation

We show, in the context of quantum combinatorial optimization, or quantum annealing, how the nonlinear Schr\"odinger-Langevin-Kostin equation can dynamically drive the system toward its ground state. We illustrate, moreover, how a frictional force of Kostin type can prevent the appearance of genuinely quantum problems such as Bloch oscillations and Anderson localization which would hinder an exhaustive search.Comment: 5 pages, 4 figures. To appear on Physical Review

A Feasibility-Preserved Quantum Approximate Solver for the Capacitated Vehicle Routing Problem

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most efficient plan for a fleet of vehicles to deliver goods to a set of customers, subject to the limited carrying capacity of each vehicle. As the number of possible solutions skyrockets when the number of customers increases, finding the optimal solution remains a significant challenge. Recently, a quantum-classical hybrid algorithm known as Quantum Approximate Optimization Algorithm (QAOA) can provide better solutions in some cases of combinatorial optimization problems, compared to classical heuristics. However, the QAOA exhibits a diminished ability to produce high-quality solutions for some constrained optimization problems including the CVRP. One potential approach for improvement involves a variation of the QAOA known as the Grover-Mixer Quantum Alternating Operator Ansatz (GM-QAOA). In this work, we attempt to use GM-QAOA to solve the CVRP. We present a new binary encoding for the CVRP, with an alternative objective function of minimizing the shortest path that bypasses the vehicle capacity constraint of the CVRP. The search space is further restricted by the Grover-Mixer. We examine and discuss the effectiveness of the proposed solver through its application to several illustrative examples.Comment: 9 pages, 8 figures, 1 tabl

Quantum Integer Programming: an Annealing approach to the Job Shop Scheduling problem

openIn this thesis i developed a complete workflow to get optimal solutions of the JSS problem. During this work i deeply analized many of the steps required in the usage of quantum annealers. In detail i tested 2 different approaches to the minor-embedding procedure and compared them with the current default euristic implemented by Dwave. I also tested an hybrid algorithm wich extract the elements of the Graver basis of the problem and then augment an initial feasible solution to obtain an optimal one. The obtained results shows that the quantum annealers can get to optimal solutions in a competitive time but, due to the limited numer of working qubits and the sparse connectivity among them, only small instances can be efficiently solved with the current hardware.In this thesis i developed a complete workflow to get optimal solutions of the JSS problem. During this work i deeply analized many of the steps required in the usage of quantum annealers. In detail i tested 2 different approaches to the minor-embedding procedure and compared them with the current default euristic implemented by Dwave. I also tested an hybrid algorithm wich extract the elements of the Graver basis of the problem and then augment an initial feasible solution to obtain an optimal one. The obtained results shows that the quantum annealers can get to optimal solutions in a competitive time but, due to the limited numer of working qubits and the sparse connectivity among them, only small instances can be efficiently solved with the current hardware

Quantum annealing for vehicle routing and scheduling problems

Metaheuristic approaches to solving combinatorial optimization problems have many attractions. They sidestep the issue of combinatorial explosion; they return good results; they are often conceptually simple and straight forward to implement. There are also shortcomings. Optimal solutions are not guaranteed; choosing the metaheuristic which best fits a problem is a matter of experimentation; and conceptual differences between metaheuristics make absolute comparisons of performance difficult. There is also the difficulty of configuration of the algorithm - the process of identifying precise values for the parameters which control the optimization process. Quantum annealing is a metaheuristic which is the quantum counterpart of the well known classical Simulated Annealing algorithm for combinatorial optimization problems. This research investigates the application of quantum annealing to the Vehicle Routing Problem, a difficult problem of practical significance within industries such as logistics and workforce scheduling. The work devises spin encoding schemes for routing and scheduling problem domains, enabling an effective quantum annealing algorithm which locates new solutions to widely used benchmarks. The performance of the metaheuristic is further improved by the development of an enhanced tuning approach using fitness clouds as behaviour models. The algorithm is shown to be further enhanced by taking advantage of multiprocessor environments, using threading techniques to parallelize the optimization workload. The work also shows quantum annealing applied successfully in an industrial setting to generate solutions to complex scheduling problems, results which created extra savings over an incumbent optimization technique. Components of the intellectual property rendered in this latter effort went on to secure a patent-protected status

Blockchain-Empowered Mobile Edge Intelligence, Machine Learning and Secure Data Sharing

Driven by recent advancements in machine learning, mobile edge computing (MEC) and the Internet of things (IoT), artificial intelligence (AI) has become an emerging technology. Traditional machine learning approaches require the training data to be collected and processed in centralized servers. With the advent of new decentralized machine learning approaches and mobile edge computing, the IoT on-device data training has now become possible. To realize AI at the edge of the network, IoT devices can offload training tasks to MEC servers. However, those distributed frameworks of edge intelligence also introduce some new challenges, such as user privacy and data security. To handle these problems, blockchain has been considered as a promising solution. As a distributed smart ledger, blockchain is renowned for high scalability, privacy-preserving, and decentralization. This technology is also featured with automated script execution and immutable data records in a trusted manner. In recent years, as quantum computers become more and more promising, blockchain is also facing potential threats from quantum algorithms. In this chapter, we provide an overview of the current state-of-the-art in these cutting-edge technologies by summarizing the available literature in the research field of blockchain-based MEC, machine learning, secure data sharing, and basic introduction of post-quantum blockchain. We also discuss the real-world use cases and outline the challenges of blockchain-empowered intelligence